I think that is a totally normal reaction to have, and I personally believe it shows respect for the animal.
Do you ever trap? I freaking hate raccoons, but I can't tell you that I enjoy shooting them in the head after I trap them. I do it A LOT but I wouldn't say I LOVE IT.
Same with deer, I love shooting deer and having a quick kill. I shoot a few does a year for meat and if I am lucky enough I will kill a buck as well. However, I have some pretty decent spots to hunt and PASS A LOT of deer. Sometimes I just don't feel like killing them. I had a fawn licking her mommas face the other day at 11 yards, and I thought to myself man I can't shoot that deer after that hahaha!
Sorry to ramble but a deer is a living breathing thing, and is a big game animal. You are KILLING IT, so I think shows you have a good head on your shoulders if you don't LIKE to watch them die..... I will never stop hunting but I will also never enjoy seeing an animal suffer.
hope my thoughts and feelings on this were clear and well presented.Thank you!